Question

64x^8+x^2 factoring polynomials

Answer 1

take out x^2, then use sum of cubes.

Answer 2

Factor out the GCF x^2 to get


64x^8+x^2 = x^2(64x^6+1)


Now factor 64x^6+1


64x^6+1


(4x^2)^3+1^3


(4x^2+1)((4x^2)^2-(4x^2)(1)+1^2)


(4x^2+1)(16x^4-4x^2+1)


So 64x^6+1 factors to (4x^2+1)(16x^4-4x^2+1)


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So 64x^8+x^2 factors to x^2(4x^2+1)(16x^4-4x^2+1)


In other words, 64x^8+x^2 = x^2(4x^2+1)(16x^4-4x^2+1)